Image fusion typically employs non-invertible neural networks to merge multiple source images into a single fused image. However, for clinical experts, solely relying on fused images may be insufficient for making diagnostic decisions, as the fusion mechanism blends features from source images, thereby making it difficult to interpret the underlying tumor pathology. We introduce FusionINN, a novel invertible image fusion framework, capable of efficiently generating fused images and also decomposing them back to the source images by solving the inverse of the fusion process. FusionINN guarantees lossless one-to-one pixel mapping by integrating a normally distributed latent image alongside the fused image to facilitate the generative modeling of the decomposition process. To the best of our knowledge, we are the first to investigate the decomposability of fused images, which is particularly crucial for life-sensitive applications such as medical image fusion compared to other tasks like multi-focus or multi-exposure image fusion. Our extensive experimentation validates FusionINN over existing discriminative and generative fusion methods, both subjectively and objectively. Moreover, compared to a recent denoising diffusion-based fusion model, our approach offers faster and qualitatively better fusion results. We also exhibit the clinical utility of our results in aiding disease prognosis.
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